Chapter 10, Problem 4MCQ

a.

To determine

To calculate who is at 50^th percentile.

Answer to Problem 4MCQ

D is at 50^th percentile.

Explanation of Solution

Given information:

The scores for a dance competition are,

Name	Score
A	87
B	91
C	90
D	88
E	79
F	82
G	94
H	81

Formula used:

Rank formula,

  $=\frac{percentile}{100}(n+1)$

Calculation:

Re-arranging the values in an ascending order,

Name	Score
E	79
H	81
F	82
A	87
D	88
C	90
B	91
G	94

Substituting the values,

  $=\frac{50}{100}\times (8+1)$

So,

  $=\frac{50}{100}\times 9$

On solving,

  $=4.5$

On rounding off,

  $\approx 5$

Comparing with the table,

D is at 50^th percentile.

Conclusion: D is at 50^th percentile.

b.

To determine

To calculate which contestants are below the 25^th percentile.

Answer to Problem 4MCQ

E is below 25^th percentile.

Explanation of Solution

Given information:

The scores for a dance competition are,

Name	Score
E	79
H	81
F	82
A	87
D	88
C	90
B	91
G	94

Formula used:

Rank formula,

  $=\frac{percentile}{100}(n+1)$

Calculation:

Substituting the values,

  $=\frac{25}{100}(8+1)$

So,

  $=\frac{25}{100}(9)$

On solving,

  $=2.25$

On rounding off,

  $\approx 2$

Comparing with the table,

E is below 25^th percentile.

Conclusion: E is below 25^th percentile.

c.

To determine

To calculate B’s percentile.

Answer to Problem 4MCQ

B is at 75^th percentile.

Explanation of Solution

Given information:

The scores for a dance competition are,

Name	Score
E	79
H	81
F	82
A	87
D	88
C	90
B	91
G	94

Formula used:

Percentile is,

  $percentile=\frac{NumberOfTermsBeforeX}{n}\times 100$

Calculation:

Substituting the values,

  $percentile=\frac{6}{8}\times 100$

On solving,

  $percentile=75$

Hence, B is at 75^th percentile.

Conclusion: B is at 75^th percentile.